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Chapter 1: Problem 3

Find each value. \(-4+7\)

Short Answer

Expert verified
The value of \(-4 + 7\) is \(3\).

Step by step solution

01

Identify the Numbers in the Expression

The numbers to deal with in this problem are \(-4\) and \(7\). More specifically, \(7\) is being added to \(-4\).
02

Adding Negative Number

Adding a negative number is the equivalent of subtracting that number's absolute value. Thus, the operation \(-4 + 7\) is equivalent to subtracting 4 from 7.
03

Perform the Subtraction

When we subtract 4 from 7, the result is 3.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Negative Numbers
Negative numbers are numbers that are less than zero. They are often used to represent values like temperatures below freezing, debts, or elevations below sea level. When dealing with negative numbers, it's crucial to understand that they behave differently when involved in arithmetic operations compared to positive numbers. Negative numbers appear with a minus sign (\(-\)) before them. For example, in the exercise where we consider the number \(-4\), this indicates that the value is four units less than zero.
  • Negative numbers decrease when added to a smaller number.
  • When combined with positive numbers, the absolute value of their difference impacts the result.
  • Understanding the sign of numbers helps to predict the outcome of arithmetic operations.
The Role of Subtraction in Integer Addition
Subtraction plays an interesting role when it comes to integer addition, especially with negative numbers. In the expression \(-4 + 7\), it may seem initially counterintuitive to associate this with subtraction. However, when adding a negative number, you essentially subtract its absolute value from the other number.
This can be visualized as taking steps backwards on a number line.
  • Subtracting a number's absolute value is synonymous with adding its negative counterpart.
  • When adding a positive number to a negative number, consider it as reducing the impact of the negative number.
  • Working with subtraction helps to simplify expressions and make calculations more intuitive.
Exploring Absolute Value
Absolute value is the measure of any number's distance from zero, without considering direction on the number line. It transforms any number into a non-negative version of itself, useful in understanding magnitudes.For example, the absolute value of both \(-4\) and \(4\) is \(4\), symbolized as \(|-4| = 4\) and \(|4| = 4\). It tells you how far the number is from zero, without regard to whether the number is positive or negative.
  • Absolute value eliminates the negative sign for computational simplicity.
  • It is particularly useful in distance measurement and comparison.
  • In this context, it aids in recognizing that \(-4 + 7\) simplifies to dealing with \(4\) subtracted from \(7\).

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Most popular questions from this chapter

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$5>2$$

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$2 \cdot 3<3 \cdot 4$$

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$8 \cdot 2 \geq 8 \cdot 1$$

Let \(x=8, y=4,\) and \(z=2 .\) Write each phrase as an algebraic expression, and evaluate it. Assume that no denominators are \(0 .\) What factor is common to all three terms? Consider the algebraic expression \(5 x y+y t+8 x y t\)

Let \(x=2, y=-3,\) and \(z=1 .\) Show that the two expressions have the same value. $$(x+y)+z ; x+(y+z)$$
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